One success factor of Kanban is its elegant simplicity for physical inventory control. However, especially in multi-variant productions inventory levels are digitally tracked. To maintain the high service levels of the Kanban systems, the digital representation in the ERP must reliably reflect the physical inventory levels and deviations should be detectable. The design of such a digitally tracked Kanban systems requires a booking logic and a method for deviation detection. Especially in multi-stage systems with several inventory levels, the design of a simple and robust Kanban logic is challenging. Thus, the paper first gives an overview of existing inventory booking strategies. Based on the strategies the effects of inventory deviations on logistical performance in classic Kanban and digitally controlled Kanban systems are discussed. Design guidelines summarize the analysis. Subsequently, three different design alternatives of a classical, digital and high resolution Kanban system are developed. These guidelines and design alternatives should enable practitioners to setup reliable Kanban systems including their digital representation.